A new trigonometric shear deformation theory for sandwich and composite plates is developed. The proposed displacement field, which is “m” parameter dependent, is assessed by performing several computations of the plate governing equations. The theory accounts for adequate distribution of the transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surface, thus a shear correction factor is not required. Plate governing equations and boundary conditions are derived by employing the principle of virtual work. The exact solutions for bending analysis are presented for sinusoidally and uniformly distributed loads. The accuracy of the present theory is ascertained by comparing it with various available results in the literature.